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On dual vector optimization and shadow prices

Published online by Cambridge University Press:  15 December 2004

Letizia Pellegrini
Letizia Pellegrini*
Affiliation:
Associate Professor, Department of Economics, University of Verona, Via Giardino Giusti 2, 37129 Verona, Italy; [email protected].
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Abstract

In this paper we present the image space analysis, based on a general separation scheme, with the aim of studying Lagrangian duality and shadow prices in Vector Optimization. Two particular kinds of separation are considered; in the linear case, each of them is applied to the study of sensitivity analysis, and it is proved that the derivatives of the perturbation function can be expressed in terms of vector Lagrange multipliers or shadow prices.

Keywords

Vector Optimizationimage spaceLagrangian dualityshadow prices.
Type
Research Article
Information
RAIRO - Operations Research , Volume 38 , Issue 4 , October 2004 , pp. 305 - 317
Copyright
© EDP Sciences, 2004

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References

Bolintineanu, S. and Craven, B.D., Linear multicriteria sensitivity and shadow costs. Optimization 26 (1992) 115–127. CrossRef
M. Ehrgott, Multicriteria Optimization. Springer, Lect. Not. Econom. Math. Syst. 491 (2000).
F. Giannessi, Theorems of the alternative, quadratic programs and complementarity problems, in Variational Inequalities and Complementarity Problems, edited by R.W. Cottle et al. J. Wiley (1980) 151–186.
Giannessi, F., Theorems of the alternative and optimality conditions. J. Optim. Theor. Appl. 42 (1984) 331–365. CrossRef
F. Giannessi, G. Mastroeni and L. Pellegrini, On the theory of vector optimization and variational inequalities. Image space analysis and separation, in Vector Variational Inequalities and Vector Equilibria. Mathematical Theories, edited by F. Giannessi. Kluwer Acad. Publ. (2000) 153–215.
Isermann, H., On some relations between a dual pair of multiple objective linear programs. Z. Oper. Res. 22 (1978) 33–41.
O.L. Mangasarian, Nonlinear Programming. SIAM Classics Appl. Math. 10 (1994).
L. Pellegrini, On Lagrangian duality in vector optimization. Optimization. Submitted.
Tanino, T., Sensitivity analysis in multiobjective optimization. J. Optim. Theor. Appl. 56 (1988) 479–499. CrossRef
Song, W., Duality for vector optimization of set valued functions. J. Math. Anal. Appl. 201 (1996) 212–225. CrossRef